Exposing the quantum geometry of spin-orbit-coupled Fermi superfluids

The coupling between a quantum particle's intrinsic angular momentum and its center-of-mass motion gives rise to the so-called helicity states that are characterized by the projection of the spin onto the direction of momentum. In this paper, by unfolding the superfluid-density tensor into its intrahelicity and interhelicity components, we reveal that the latter contribution is directly linked with the total quantum metric of the helicity bands. We consider both Rashba and Weyl spin-orbit couplings across the BCS-BEC crossover and show that the geometrical interhelicity contribution is responsible for up to a quarter of the total superfluid density. We believe this is one of those elusive effects that may be measured within the highly tunable realm of cold Fermi gases.